Washington (CNN) -- Two major civil liberties groups filed a lawsuit Tuesday challenging the government's asserted authority to kill U.S. citizens living abroad who are designated as terrorists.

The American Civil Liberties Union and the Center for Constitutional Rights announced they represent the father of influential Islamic cleric Anwar al-Awlaki, believed to be living in Yemen, who may be targeted by U.S. government drones.

U.S. officials believe al-Awlaki, a Yemeni-American, influenced Maj. Nidal Hasan, the man accused of killing 13 people in the 2009 Fort Hood shootings, and played a more active role in Umar Farouk Abdul-Mutallab's attempted bombing of a U.S. airliner on Christmas Day 2009.

Officials also believe al-Awlaki inspired Faisal Shahzad, who has pleaded guilty to federal terrorism charges in the attempted car bomb attack in Times Square in May, as well as several others.

The ACLU and CCR announced the challenge to the government's plan to use lethal force against U.S. citizens "located far from any battlefield without charge, trial, or judicial process of any kind," a statement from the groups said.

"President Obama is claiming the power to act as judge, jury, and executioner while suspending any semblance of due process," said Vince Warren, executive director of the CCR.

The two groups and al-Awlaki's father, Nasser al-Awlaki, are particularly concerned about the use of drones to target civilian al-Qaeda supporters. Unmanned drones are frequently used in the border region between Afghanistan and Pakistan, where Taliban and other insurgents are believed to be operating.

The suit specifically challenges the law that prohibits attorneys from providing representation for al-Awlaki without first seeking a license from the Treasury Department's Office of Foreign Asset Control.

The office, which labeled al-Awlaki a "specially designated global terrorist," has so far not granted the groups a license.

"The government is targeting an American citizen for death without any legal process whatsoever, while at the same time impeding lawyers from challenging that death sentence," said ACLU Executive Director Anthony Romero.

The Justice Department, which is expected to defend the administration against the lawsuit, had no immediate comment.